All charges are equal in magnitude, fixed in place, and equidistance along the x

Question

All charges are equal in magnitude, fixed in place, and equidistance along the x-axis from the y axis. Consider the electrostatic force on the middle charge P from the two particles along the x-axis. For situation 1, answer the following questions: Draw a force diagram for charge P. Are the magnitudes of these forces (say F) due to each charge the same or different? Is the magnitude of the net force on the middle charge equal to, greater than, or less than 2F? Do the x components of the two forces add or cancel? Do their y components add or cancel? What is the direction of that net force? Now repeat the same questions for situation 2. Now repeat the same questions for situation 3. Now repeat the same questions for situation 4.

Explanation / Answer

a) For situation 1:
•   Magnitude of forces due to each charge is same.
•   Magnitude of net force = 2Fcos45 < 2F
•   X-components will get cancel
•   Y-component will add
•   Direction of net force is along +y-axis

b) For situation 2:
•   Magnitude of forces due to each charge is same.
•   Magnitude of net force = 2Fcos45 < 2F
•   X-components will get cancel
•   Y-component will add
•   Direction of net force is along -y-axis

c) For situation 3:
•   Magnitude of forces due to each charge is same.
•   Magnitude of net force = 2Fcos45 < 2F
•   X-components will add
•   Y-component will get cancel
•   Direction of net force is along +x-axis

d) For situation 4:
•   Magnitude of forces due to each charge is same.
•   Magnitude of net force = 2Fcos45 < 2F
•   X-components will add
•   Y-component will get cancel
•   Direction of net force is along -x-axis

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